Monday, April 17, 2006

JICS/MATH POSITION CANDIDATE COLLOQUIUM
Time: 3:35 pm
Room: 214 Ayres Hall
Speaker: Professor Petr Plechac, University of Warwick
Title: Numerical analysis of coarse-graining for stochastic dynamics

In many applications a microscopic (stochastic) model is often coupled with continuum description (using PDEs) on larger scales. Efficient simulations on such systems often require reduction of computational degrees of freedom. In this talk I will discuss some general mathematical issues arising in computations where the microscopic Markov process is approximated by a hierarchy of coarse-grained processes. I shall present mathematical tools (e.g., information-type estimates) for error estimation of the coarse-graining procedure. The techniques will be explained in specific examples of lattice spin dynamics and various types of error control will be discussed. It will be demonstrated that computational implementation of coarse-grained processes leads to significant CPU speed up of simulations, including e.g., estimation of switching times or nucleation of new phases. Numerical evidence supported with rigorous analysis thus indicates regimes in which the coarse-grained Monte Carlo algorithm probes efficiently energy landscape and provides accurate approximation of sampled quantities.

Refreshments will be served at 3:00 pm in 119 Ayres Hall.

Wednesday, April 19, 2006

TOPOLOGY SEMINAR
Time: 1:25 pm - 2:15 pm
Room: 309A Ayres Hall
Speaker: Professor Nikolay Brodskiy
Title: Amenability of countable groups II

ANALYSIS SEMINAR
Time: 3:35 pm - 4:25 pm
Room: 309A Ayres Hall
Speaker: Professor Carl Sundberg
Title: “Why a Riemann surface is a Riemann surface.”

Thursday, April 20, 2006

UNDERGRADUATE HONORS SEMINAR
Time: 9:30 am – 11:10 am
Room: 309B Ayres Hall
Speaker: Chad Jones, University of Tennessee
Title: A Multi-Level Cache Model for Run-Time Optimization of Remote Visualization

Remote visualization is an enabling technology aiming to resolve the barrier of physical distances in visualization collaboration. While many researchers have developed innovative algorithms for remote visualization, less previous work has focused on systematically investigating optimal configurations of remote visualization architectures. Our study focuses on caching and prefetching, important aspects of such architecture design, in order to optimize the fetch time in a remote visualization system. Caching for remote visualization is unique and complex, and unlike a processor cache indexed by monolithic memory addresses, caches for remote visualization need to manage requests indexed by an application-dependent number of parameters, like time step, view angle, iso-value, and etc. In addition, the size of the requested data in a remote visualization is usually request-dependent, while processor caches strictly deal with cache lines of a constant size. We have discovered, through actual experimentation and numerical simulation, ways to systematically evaluate and search for optimal configurations under various scenarios, which allows our infrastructure to adaptively optimize the caching architecture as the remote visualization system changes.

Friday, April 21, 2006

TOPOLOGY SEMINAR
Time: 12:20 pm - 1:10 pm
Room: 209B Ayres Hall
Title: Coarse Geometry and Topology III
Speaker: Christian Hoffland, University of Tennessee

JICS/MATH POSITION CANDIDATE COLLOQUIUM
Time: 3:35 pm – 4:30 pm
Room: 214 Ayres Hall
Title: Spatial solitons, light bullets, optical vortices, and semi-discrete solitons supported by periodic quadratically nonlinear crystals
Speaker: Professor Nicolae Panoiu, Research Scientist at Columbia University, Department of Applied Physics and Applied Mathematics

Solitons are localized excitations that are not distorted upon propagation in a nonlinear medium. In optical media, solitons form either through a balance between dispersive and self-phase modulation effects (temporal solitons) or, in the spatial domain, as a result of the balance of diffraction and nonlinear self-focusing (spatial solitons). One such optical medium, which has many applications to frequency-doubling devices, phase-controlled transistors, or all-optical switches, consists of a quadratically nonlinear crystal with periodic variation of linear and nonlinear optical constants (index of refraction and quadratic susceptibility). The talk will review recent work on the existence, dynamics, and stability of one- and two-dimensional spatial solitons, light bullets, and optical vortices supported by such spatially modulated quadratically nonlinear crystals. In particular, by employing an averaging approach based on perturbation theory, I will show that the stability of these nonlinear excitations is strongly affected by effective cubic nonlinearities induced by the parametric interaction of the optical beams. I also demonstrate that if the optical constants of the crystal vary in a plane transverse to the direction of wave propagation, the nonlinear crystal supports a new type of stable solitons, called semi-discrete solitons. Twisted bound states of these fundamental solitons are found, too. Finally, technological applications to photonic devices will be discussed.

Refreshments will be served at 3:00 pm in 119 Ayres Hall.